Finite Group Databasebeta

← #15788295

Subgroups — #15788295

Order 3328.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718642C211yesmaximal, characteristic, complemented
2C2×#11718611C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic13C211yesmaximal, characteristic
5#13113104C211yesmaximal, characteristic, complemented
6#13113089C211yesmaximal, characteristic, complemented
7#13113081C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113070C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113065C211yesmaximal, characteristic, complemented
14#13113058C211yesmaximal, characteristic
15C2×C13×#399C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C13×#399C418yescomplemented
34C2×C13×#95C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52#11718642—24no—
53C4⋊C4×Dic13—24no—
54#11718611—24no—
55C22⋊C4×Dic13—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13—22no—
64C23×Dic13—22no—
65C23×Dic13—22no—
66C23×Dic13—22no—
67C23×Dic13—22no—
68C23×Dic13—41no—
69C23×Dic13—41no—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C4⋊C4C2×C414yescomplemented
85C2×C13×C4⋊C4C2×C414yescomplemented
86C2×C13×C4⋊C4C2×C414yescomplemented
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—41no—
92C2×C13×C22⋊C4—41no—
93C2×C13×C22⋊C4C2×C414yes—
94C2×C13×C22⋊C4C2×C414yes—
95C2×C13×C22⋊C4C2×C414yes—
96C2×C22⋊Dic13—22no—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—22no—
99C2×C22⋊Dic13—22no—
100C2×C22⋊Dic13—22no—
101C2×C22⋊Dic13—22no—
102C2×C22⋊Dic13—41no—
103C2×C22⋊Dic13—41no—
104C2×C22⋊Dic13Q814yes—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—41no—
112C2×C4⋊Dic13—41no—
113C2×C4⋊Dic13D414yes—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—41no—
124C2×C4×Dic13—41no—
125C2×C4×Dic13—41no—
126C13×#95C2×C414yescomplemented
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#88071—41no—
142#88071—41no—
143#88071D414yes—
144#14178—131nomaximal, Sylow
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13C22×C412yes—
158C24×C13C2×Q812yes—
159C24×C13#4112yes—
160C24×C13C2411yescharacteristic
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C22×C412yes—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13#4112yes—
202C22×C4×C13#4112yes—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—28no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—44no—
251C22×Dic13—44no—
252C22×Dic13—44no—
253C22×Dic13—44no—
254C22×Dic13—44no—
255C22×Dic13—44no—
256C22×Dic13C2×D412yes—
257C22×Dic13C2×D412yes—
258C22×Dic13C2×D412yes—
259C22×Dic13C2×D412yes—
260C22×Dic13C2×Q812yes—
261C22×Dic13C2×Q812yes—
262C22×Dic13#4112yes—
263C22×Dic13#4112yes—
264C22×Dic13#4112yes—
265C22×Dic13#4112yes—
266C13×C4⋊C4—28no—
267C13×C4⋊C4—28no—
268C13×C4⋊C4—44no—
269C13×C22⋊C4—28no—
270C13×C22⋊C4—28no—
271C13×C22⋊C4—44no—
272C22⋊Dic13—28no—
273C22⋊Dic13—44no—
274C22⋊Dic13—44no—
275C4⋊Dic13—28no—
276C4⋊Dic13—44no—
277C4⋊Dic13—44no—
278C4×Dic13—28no—
279C4×Dic13—44no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#399D1311yescharacteristic
283C2×#387—131no—
284C2×#385—131no—
285C2×C4×C4⋊C4—131no—
286C2×C4×C22⋊C4—131no—
287#1445—131no—
288#1441—131no—
289#1439—131no—
290#1437—131no—
291#1437—131no—
292#1436—131no—
293#1436—131no—
294#1436—131no—
295C4⋊#95—131no—
296C22⋊#95—131no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13C4×Q814yes—
332C23×C13C23×C411yescharacteristic
333C23×C13C22×D411yescharacteristic
334C23×C13C22×D411yescharacteristic
335C23×C13C22×Q811yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13C2×#4111yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13H(5,𝔽2)11yescharacteristic
344C23×C13H(5,𝔽2)11yescharacteristic
345C23×C13H(5,𝔽2)11yescharacteristic
346C23×C132−1+411yescharacteristic
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13C4×D414yes—
388C2×C4×C13C4×D414yes—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—416no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13C22⋊Q814yes—
445C2×Dic13#12314yes—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4C2×D1311yescharacteristic
451C22×C4⋊C4C2×D1311yescharacteristic
452C22×C4⋊C4C2×D1311yescharacteristic
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4C2×D1311yescharacteristic
457C22×C22⋊C4C2×D1311yescharacteristic
458C22×C22⋊C4C2×D1311yescharacteristic
459C22×C42—131no—
460C22×C42—131no—
461C22×C42—131no—
462C22×C42—131no—
463#399Dic1318yescomplemented
464#387—264no—
465#385—264no—
466C4×C4⋊C4—264no—
467C4×C22⋊C4—264no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95C2×D1311yescharacteristic
486C22×C13—24no—
487C22×C13—24no—
488C22×C13—24no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13C2×C4×D411yescharacteristic
502C22×C13C2×C4×D411yescharacteristic
503C22×C13C2×C4×Q811yescharacteristic
504C22×C13C4×#4111yescharacteristic
505C22×C13C4×#4111yescharacteristic
506C22×C13#51811yescharacteristic
507C22×C13#52011yescharacteristic
508C22×C13C2×C22⋊Q811yescharacteristic
509C22×C13C2×#12311yescharacteristic
510C22×C13#52511yescharacteristic
511C22×C13#52511yescharacteristic
512C22×C13#52911yescharacteristic
513C22×C13#52911yescharacteristic
514C22×C13#52911yescharacteristic
515C22×C13#53311yescharacteristic
516C22×C13#53811yescharacteristic
517C22×C13#53911yescharacteristic
518C22×C13#54011yescharacteristic
519C22×C13#54211yescharacteristic
520C22×C13D4211yescharacteristic
521C22×C13#54611yescharacteristic
522C22×C13#54611yescharacteristic
523C22×C13#54711yescharacteristic
524C22×C13D4×Q811yescharacteristic
525C22×C13#55011yescharacteristic
526C22×C13#55011yescharacteristic
527C22×C13#55111yescharacteristic
528C22×C13#55111yescharacteristic
529C22×C13#55111yescharacteristic
530C22×C13#55211yescharacteristic
531C22×C13#55211yescharacteristic
532C22×C13#55411yescharacteristic
533C22×C13#55411yescharacteristic
534C22×C13#55411yescharacteristic
535C22×C13#55911yescharacteristic
536C4×C13—24no—
537C4×C13—24no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542Dic13—24no—
543Dic13—24no—
544Dic13—42no—
545Dic13—42no—
546Dic13—42no—
547Dic13—42no—
548Dic13—81no—
549Dic13—81no—
550C25C22×D1311yescharacteristic
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4—262no—
560C23×C4—262no—
561C23×C4—262no—
562C23×C4—262no—
563C23×C4—262no—
564C23×C4—521no—
565C23×C4—521no—
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—134no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—521no—
586C2×C4⋊C4—521no—
587C2×C4⋊C4C2×Dic1314yescomplemented
588C2×C4⋊C4C2×Dic1314yescomplemented
589C2×C4⋊C4C2×Dic1314yescomplemented
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—134no—
597C2×C22⋊C4—262no—
598C2×C22⋊C4—262no—
599C2×C22⋊C4—262no—
600C2×C22⋊C4—262no—
601C2×C22⋊C4—262no—
602C2×C22⋊C4—262no—
603C2×C22⋊C4—521no—
604C2×C22⋊C4—521no—
605C2×C22⋊C4C2×Dic1314yes—
606C2×C22⋊C4C2×Dic1314yes—
607C2×C22⋊C4C2×Dic1314yes—
608C2×C42—262no—
609C2×C42—262no—
610C2×C42—262no—
611C2×C42—262no—
612C2×C42—262no—
613C2×C42—262no—
614C2×C42—262no—
615C2×C42—262no—
616C2×C42—262no—
617C2×C42—521no—
618C2×C42—521no—
619C2×C42—521no—
620#95—134no—
621#95—262no—
622#95—262no—
623#95—262no—
624#95—262no—
625#95—262no—
626#95—262no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—521no—
633#95—521no—
634#95—521no—
635#95—521no—
636#95—521no—
637#95C2×Dic1314yescomplemented
638C2×C13—44no—
639C2×C13C4×#12311yescharacteristic
640C2×C13C4×C22⋊Q811yescharacteristic
641C2×C13#233511yescharacteristic
642C2×C13#235911yescharacteristic
643C2×C13#236011yescharacteristic
644C2×C13#236611yescharacteristic
645C2×C13#236811yescharacteristic
646C2×C13#241811yescharacteristic
647C2×C13#242311yescharacteristic
648C2×C13#244911yescharacteristic
649C2×C13#245411yescharacteristic
650C2×C13#247111yescharacteristic
651C2×C13#247911yescharacteristic
652C2×C13#257511yescharacteristic
653C2×C13#258911yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24Q8×D1312yes—
667C24#613112yes—
668C24C22×Dic1312yes—
669C24C23×D1311yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—132no—
703C22×C4—132no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—268no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—524no—
760C22×C4—524no—
761C22×C4—524no—
762C22×C4—524no—
763C22×C4—524no—
764C22×C4—524no—
765C22×C4D4×D1312yes—
766C22×C4D4×D1312yes—
767C22×C4#612912yes—
768C22×C4#612912yes—
769C22×C4C22×Dic1312yes—
770C22×C4C22×Dic1312yes—
771C22×C4C22×Dic1312yes—
772C22×C4C22×Dic1312yes—
773C22×C4C22×Dic1312yes—
774C22×C4C22×Dic1312yes—
775C4⋊C4—28no—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—268no—
779C4⋊C4—524no—
780C4⋊C4—524no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—44no—
784C22⋊C4—268no—
785C22⋊C4—524no—
786C22⋊C4—524no—
787C42—268no—
788C42—524no—
789C42—524no—
790C42—524no—
791C13#1417811yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23Q8×Dic1314yes—
827C23C2×D4×D1311yescharacteristic
828C23C2×D4×D1311yescharacteristic
829C23C2×#612911yescharacteristic
830C23C2×#612911yescharacteristic
831C23#8825111yescharacteristic
832C23#8825111yescharacteristic
833C23C2×Q8×D1311yescharacteristic
834C23C2×#613111yescharacteristic
835C23#41×D1311yescharacteristic
836C23#41×D1311yescharacteristic
837C23#41×D1311yescharacteristic
838C23#41×D1311yescharacteristic
839C23#8825611yescharacteristic
840C23#8825711yescharacteristic
841C23C23×Dic1311yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—134no—
883C2×C4—134no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—5216no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4D4×Dic1314yes—
940C2×C4D4×Dic1314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22#1171932711yescharacteristic
957C22#1171932911yescharacteristic
958C22D13×C22⋊Q811yescharacteristic
959C22#1171933211yescharacteristic
960C22#1171933511yescharacteristic
961C22#1171933711yescharacteristic
962C22#1171934011yescharacteristic
963C22#1171934111yescharacteristic
964C22#1171934111yescharacteristic
965C22#1171934211yescharacteristic
966C22#1171934211yescharacteristic
967C22#1171934711yescharacteristic
968C22#1171935411yescharacteristic
969C22#1171935411yescharacteristic
970C22#1171935511yescharacteristic
971C22D13×#12311yescharacteristic
972C22#1171935911yescharacteristic
973C22#1171936011yescharacteristic
974C22#1171936111yescharacteristic
975C22#1171936211yescharacteristic
976C22#1171936311yescharacteristic
977C22#1171936511yescharacteristic
978C22#1171936711yescharacteristic
979C22#1171936811yescharacteristic
980C22#1171941811yescharacteristic
981C22#1171942211yescharacteristic
982C22#1171942311yescharacteristic
983C22#1171942311yescharacteristic
984C22C2×D4×Dic1311yescharacteristic
985C22C2×D4×Dic1311yescharacteristic
986C22#1171950311yescharacteristic
987C22C2×Q8×Dic1311yescharacteristic
988C22#41×Dic1311yescharacteristic
989C22#41×Dic1311yescharacteristic
990C22#1171953211yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—264no—
998C4—264no—
999C4—522no—
1000C4—522no—
1001C4—522no—
1002C4—522no—
1003C4—1041no—
1004C4—1041no—
1005C2—44no—
1006C2#123×Dic1311yescharacteristic
1007C2C22⋊Q8×Dic1311yescharacteristic
1008C2#1311763011yescharacteristic
1009C2#1311783211yescharacteristic
1010C2#1311784511yescharacteristic
1011C2#1311790111yescharacteristic
1012C2#1311792111yescharacteristic
1013C2#1311830111yescharacteristic
1014C2#1311835411yescharacteristic
1015C2#1311864811yescharacteristic
1016C2#1311870311yescharacteristic
1017C2#1311894011yescharacteristic
1018C2#1311907011yescharacteristic
1019C2#1312012611yescharacteristic
1020C2#1312028011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#399C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#399D13
hypocenterC13#14178
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#399

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11718642C2semidirect
3. C2×C4⋊C4×Dic13C2semidirect
5. #13113104C2semidirect
6. #13113089C2semidirect
10. #13113070C2semidirect
11. #13113070C2semidirect
12. #13113068C2semidirect
13. #13113065C2semidirect
33. C13×#399C4semidirect
84. C2×C13×C4⋊C4C2×C4semidirect
85. C2×C13×C4⋊C4C2×C4semidirect
86. C2×C13×C4⋊C4C2×C4semidirect
126. C13×#95C2×C4semidirect
463. #399Dic13semidirect
587. C2×C4⋊C4C2×Dic13semidirect
588. C2×C4⋊C4C2×Dic13semidirect
589. C2×C4⋊C4C2×Dic13semidirect
637. #95C2×Dic13semidirect
791. C13#14178semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117186422
C2×#117186112
C2×C4⋊C4×Dic132
C2×C22⋊C4×Dic132
#131131042
#131130892
#131130812
#131130732
#131130702
#131130682
#131130652
#131130582
C2×C13×#3992
#1417813